JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
\(A\) particle is moving in the \(x y\)-plane along a curve \(C\) passing through the point \((3,3)\). The tangent to the curve \(C\) at the point \(P\) meets the \(x\)-axis at \(Q\). If the \(y\)-axis bisects the segment \(P Q\), then \(C\) is a parabola with
- A length of latus rectum \(3\)
- B length of latus rectum \(6\)
- C focus \(\left(\frac{4}{3}, 0\right)\)
- D focus \(\left(0, \frac{3}{4}\right)\)
Answer & Solution
Correct Answer
(A) length of latus rectum \(3\)
Step-by-step Solution
Detailed explanation
Let Point \(P ( x , y )\) \(Y-y=y^{\prime}(X-x)\) \(Y =0 \Rightarrow X = x -\frac{ y }{ y ^{\prime}}\) \(Q \left( x -\frac{ y }{ y ^{\prime}}, 0\right)\) Mid Point of \(PQ\) lies on y axis \(x-\frac{y}{y^{\prime}}+x=0\)…
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